Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{(n^{-1})^{-5}}}{{n^{2}x}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(n^{-1})^{-5} = n^{5}}$ In the denominator, we can use the distributive property of exponents. ${n^{2}x = n^{2}x}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(n^{-1})^{-5}}}{{n^{2}x}} = \dfrac{{n^{5}}}{{n^{2}x}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}}}{{n^{2}x}} = \dfrac{{n^{5}}}{{n^{2}}} \cdot \dfrac{{1}}{{x}} = n^{{5} - {2}} \cdot x^{- {1}} = n^{3}x^{-1}$.